Old assertion of right making us cry out (7)
I believe the answer is:
exclaim
'cry out' is the definition.
(synonyms)
'old assertion of right' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'assertion of right' becomes 'claim' (I've seen this before).
'ex'+'claim'='EXCLAIM'
'making us' acts as a link.
(Other definitions for exclaim that I've seen before include "Blurt out" , "Speak sharply" , "Express surprise" , "Speak suddenly" , "Call" .)